J. Cobb [1]} constructed a Cantor set in \(\mathbb {R}^3\)  such that its projection to
every 2-plane is 1-dimensional.
Cobb asked
[1]}:
“Could there be Cantor sets all of whose projections
are connected, or even cells?
...given \(n>m>k>0\) , does there exist a Cantor set in \(\mathbb {R}^n\)  such that
each of its projections
into \(m\) -planes is exactly \(k\) -dimensional?”
(Following [3]}, we call these sets
\((n,m,k)\) -sets.)
Examples of
\((n, m, m-1)\) - and \((n, n-1, k)\) -Cantor sets
are given in [4]} and [3]}, respectively.
The known \((n,m,k)\) -Cantor sets
[6]},
[7]},
[1]},
[4]},
[3]}
are tame by constructions and by
[11]} (see Statement REF ;
for the notions of tame and wild, see
Definition REF ).
